TEL AVIV, Israel — The administration has been engaged for weeks in detailed and substantive conversations about new legislation to arm the Syrian rebels — though it hasn’t taken a public position on a new bill that seeks to do just that, The Post has learned.

Rep. Eliot Engel (D-Bronx), the top Democrat on the House International Relations Committee, introduced the legislation last week along with Rep. Mike Rogers (R-Mich.), the top Republican on the House Intelligence Committee.

The White House has resisted calls to arm the rebels for months, arguing the situation is too unstable and uncertain and could put weapons into the hands of terrorists.

But Engel said he shared information on the bill with the administration for weeks.

“We kept them informed of every move,” Engel told The Post from Tel Aviv, where he flew aboard Air Force One on a visit with President Obama. “We didn’t want it to be a surprise or be an adversarial thing.”

Engel didn’t say if he made any changes for the White House but noted that “we listened to suggestions from lots of people to try to get more things on.”

Arming the rebels may well be risky, the lawmaker said, but “to do nothing is even riskier.”

The bill provides arms, training and intelligence aid.

“The rebels are going to win,” Engel said. “If the United States does not help them beforehand, I don’t think we’ll have influence afterward.”

Zalman Shoval, a key adviser to Israeli Prime Minister Benjamin Netanyahu, told The Post there is “no space” between the United States and Israel on the issue of arming the rebels, referring to the administration’s opposition to this point.

“Those arms, or many of them, are going to fall into the hands of the extremists,” he said, increasing the risk on Israel’s border.